This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming obtained from centrality equations of the form $X S + SX = 2 \nu W$, where $W$ is a fixed positive definite matrix and $\nu>0$ is a parameter, under the assumption that the problem has a strictly complementary primal-dual optimal solution. … Read more
This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming obtained from centrality equations of the form $X^{1/2}S X^{1/2} = \nu W$, where $W$ is a fixed positive definite matrix and $\nu>0$ is a parameter, under the assumption that the problem has a strictly complementary primal-dual optimal solution. It is shown … Read more
By using a variational method based on Ekeland’s principle, we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces, and … Read more
Recently,Tseng extended a class of merit functions for the nonlinear complementarity problem to semidefinite complementarity problem (SDCP), showing some properties under suitable assumptions. Yamashita and Fukushima also presented other properties. In this paper, we propose a new class of merit functions for the SDCP, and prove some of those properties, under weaker hypothesis. Particularly, we … Read more